Class 9 Maths — Chapter 9: CIRCLES

What you'll learn

• ▸Angle Subtended by a Chord
• ▸Theorem 9.1: Equal Chords and Angles at the Centre
• ▸Theorem 9.2: Converse of Theorem 9.1
• ▸Theorem 9.3: Perpendicular from Centre to a Chord
• ▸Theorem 9.4: Line Bisecting a Chord from the Centre
• ▸Theorem 9.5: Equal Chords and their Distance from the Centre
• ▸Theorem 9.6: Equidistant Chords

Chapter Summary

--- PAGE 1 --- CHAPTER 9 CIRCLES 9.1 Angle Subtended by a Chord at a Point You have already studied about circles and its parts in Class VI. Take a line segment PQ and a point R not on the line containing PQ. Join PR and QR (see Fig. 9.1). Then ∠ PRQ is called the angle subtended by the line segment PQ at the point R. What are angles POQ, PRQ and PSQ called in Fig. 9.2? ∠ POQ is the angle subtended by the chord PQ at the centre O, ∠ PRQ and ∠ PSQ are respectively the angles subtended by PQ at points R and S on the major and minor arcs PQ. R P Q Fig. 9.1 R O P Q S Fig. 9.2 Let us examine the relationship between the size of the chord and the angle subtended by it at the centre. You may see by drawing different chords of a circle and angles subtended by them at the centre that the longer is the chord, the bigger will be the angle subtended by it at the centre. What will happen if you take two equal chords of a circle? Wi…

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Illustrate chord properties visually. Get Solution →
2. Discover circles in nature. Get Solution →
3. Prove two triangles are congruent. Get Solution →
4. What is the relationship between the length of a chord and the angle it subtends at the centre, according to the text? Get Solution →
5. What does Theorem 9.1 state about equal chords of a circle? Get Solution →
6. What is the meaning of the abbreviation 'CPCT' used in the chapter? Get Solution →
7. According to Theorem 9.3, what does the perpendicular from the centre of a circle to a chord do to the chord? Get Solution →
8. What is the definition of the distance from a point to a line? Get Solution →

Did you know?

• 💡 Ancient mathematicians used sticks and shadows to measure Earth's circular size.
• 💡 The world's largest Ferris wheel, a perfect circle, is in Dubai.
• 💡 Some tiny bacteria swim in perfect circles when they are confused.
• 💡 A pizza slice is a "sector" of a circle, while the crust edge is an "arc".
• 💡 Even before wheels, people moved heavy objects on logs, acting like rolling circles.

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